Second main theorem and uniqueness problem of zero-order meromorphic mappings for hyperplanes in subgeneral position
Bull. Korean Math. Soc. 2018 Vol. 55, No. 1, 205-226
Published online January 31, 2018
Thi Tuyet Luong, Dang Tuyen Nguyen, Duc Thoan Pham
National University of Civil Engineering, National University of Civil Engineering, National University of Civil Engineering
Abstract : In this paper, we show the Second Main Theorems for zero-order meromorphic mapping of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ intersecting hyperplanes in subgeneral position without truncated multiplicity by considering the $p$-Casorati determinant with $p\in\mathbb C^m$ instead of its Wronskian determinant. As an application, we give some unicity theorems for meromorphic mapping under the growth condition ``order=0". The results obtained include $p$-shift analogues of the Second Main Theorem of Nevanlinna theory and Picard's theorem.
Keywords : second main theorem, Nevanlinna theory, Casorati determinant, zero-order meromorphic mapping, hyperplanes
MSC numbers : Primary 53A10; Secondary 53C42, 30D35, 32H30
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